Mastering Calculus Derivatives: Essential Rules for Computing f'(x)

f'(x) or dy/dx or y’

In calculus, the notation f'(x), dy/dx, or y’ represents the derivative of a function f with respect to x

In calculus, the notation f'(x), dy/dx, or y’ represents the derivative of a function f with respect to x. It basically indicates the rate at which the function is changing at a particular point.

To calculate the derivative, you need to apply the rules of differentiation. Here are some common rules that can be applied depending on the function:

1. Power Rule: If f(x) = x^n (where n is a constant), then f'(x) = n*x^(n-1). For example, if f(x) = x^2, then f'(x) = 2*x^(2-1) = 2x.

2. Constant Rule: If f(x) = c (where c is a constant), then f'(x) = 0. This means that the derivative of a constant is always zero.

3. Sum/Difference Rule: If f(x) = g(x) ± h(x) (where g(x) and h(x) are functions), then f'(x) = g'(x) ± h'(x). Essentially, you differentiate each function separately and then add or subtract their derivatives together.

4. Product Rule: If f(x) = g(x) * h(x), then f'(x) = g'(x) * h(x) + g(x) * h'(x). This rule is used to find the derivative of a product of two functions.

5. Quotient Rule: If f(x) = g(x) / h(x), then f'(x) = (g'(x) * h(x) – g(x) * h'(x)) / (h(x))^2. This rule is used to find the derivative of a quotient of two functions.

These are just a few of the primary rules of differentiation, and there are other rules and techniques available depending on the complexity of the function. It’s important to practice and gain a deeper understanding of these rules in order to effectively calculate derivatives in calculus.

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